Suppose that three compact discs are removed from their cases, and that after they have been played, they are put back into the three empty cases in a random manner. Determine the probability that at least one of the CD’s will be put back into the proper cases.

The probability that at least one of the CD'S will be put back into the proper cases is 2/3

Step-by-step explanation:

The total amount of possibilities of putting back the CD's is equal to the total amount of ways of ordering a set of 3 elements, in other words, 3! = 6. In 4 of those 6 ways, at least one of the CD's is put back properly:

- All CD's are put back into the proper cases

- First disc is put back into its proper cases, Second disc is put back in third's position, and third  disc is put back in second's position.

- Second Disc is put back correctly, and first and third not

- Thir disc is put back correctly and first and second got 'swapped'.

Thus, the probability that at least one of the CD'S will be put back into the proper cases is 4/6 = 2/3.